A complete system of structural invariants for regularizable singular systems
María Isabel García Planas, Alexander Diaz-Lopez, C. Miner ́ ia · 2007
Let (E;A;B;C) be a quadruple of matrices with E;A 2 Mn(C), B 2 Mn£m(C), C 2 Mp£n(C) representing a singular time-invariant linear system, E ˙ x = Ax + Bu, y = Cx. In this paper we present a collection of invariants for singular systems in terms of ranks of certain matrices, that permit us to reduce the system in a canonical form in such a way that the system is decomposed in following five independent subsystems: i) controllable and observable system, ii) controllable non observable system, iii) observable non controllable system, iv) Jordan system v) completely singular system.